We present H-band polarimetric imagery of UX Tau A taken with HiCIAO/AO188 on the Subaru Telescope. UX Tau A has been classified as a pre-transitional disk object, with a gap structure separating its inner and outer disks. Our imagery taken with the 0.15" (21 AU) radius coronagraphic mask has revealed a strongly polarized circumstellar disk surrounding UX Tau A which extends to 120 AU, at a spatial resolution of 0.1" (14 AU). It is inclined by 46 degrees plus or minus 2 degrees as the west side is nearest. Although SED modeling and sub-millimeter imagery suggested the presence of a gap in the disk, with the inner edge of the outer disk estimated to be located at 25 - 30 AU, we detect no evidence of a gap at the limit of our inner working angle (23AU) at the near-infrared wavelength. We attribute the observed strong polarization (up to 66 %) to light scattering by dust grains in the disk. However, neither polarization models of the circumstellar disk based on Rayleigh scattering nor Mie scattering approximations were consistent with the observed azimuthal profile of the polarization degrees of the disk. Instead, a geometric optics model of the disk with nonspherical grains with the radii of 30 micrometers is consistent with the observed profile. We suggest that the dust grains have experienced frequent collisional coagulations and have grown in the circumstellar disk of UX Tau A.